Linear Operators: Spectral theory |
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Page 860
... unit e . We shall show how a unit may be adjoined to such an algebra so that the extended algebra is a B - algebra . Let X be an alge- bra satisfying all the requirements of a B - algebra except that X has no unit . Let X1 = XX where is ...
... unit e . We shall show how a unit may be adjoined to such an algebra so that the extended algebra is a B - algebra . Let X be an alge- bra satisfying all the requirements of a B - algebra except that X has no unit . Let X1 = XX where is ...
Page 979
... unit I in B ( L2 ( R ) ) nor does its closure T ( L1 ( R ) ) in the uniform operator topology contain the unit . The algebra A is , by definition , the B - algebra obtained by adjoining the unit I to T ( L1 ( R ) ) . Its elements have ...
... unit I in B ( L2 ( R ) ) nor does its closure T ( L1 ( R ) ) in the uniform operator topology contain the unit . The algebra A is , by definition , the B - algebra obtained by adjoining the unit I to T ( L1 ( R ) ) . Its elements have ...
Page 1493
... unit circle under the map 1 includes a set of m analytic arcs all intersecting at equal angles л / m at the point 2. If m > 1 , not all of these arcs can possibly lie along the real axis . Hence we must have m = 1 , so that 1 is one ...
... unit circle under the map 1 includes a set of m analytic arcs all intersecting at equal angles л / m at the point 2. If m > 1 , not all of these arcs can possibly lie along the real axis . Hence we must have m = 1 , so that 1 is one ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero